Properties of 3D shapes

A face is a flat (or curved) surface, an edge is where two faces meet, and a vertex is a corner.

For shapes with flat faces, faces + vertices − edges = 2.

Example: find the number of faces, edges and vertices of a hexagonal prism.

1. Faces: 2 hexagons + 6 rectangles = 8
2. Vertices: 6 on each hexagon = 12
3. Edges: 6 on each hexagon + 6 joining them = 18

Check: 8 + 12 − 18 = 2.

A net is a flat shape that folds up to make a 3D shape. Each face of the 3D shape appears once in the net.

• A cube's net has 6 squares (there are 11 different ones).
• A triangular prism's net has 3 rectangles in a row, with a triangle on each side of the middle rectangle.
• A cylinder's net has 2 circles and a rectangle. The rectangle's length is the circumference of the circles.

Example: a net is made of four equilateral triangles. What 3D shape does it make?

1. 4 triangular faces, with 3 meeting at each corner
2. A tetrahedron (triangular-based pyramid)

A 3D shape can be drawn as three flat views:

• the plan: looking down from above
• the front elevation: looking from the front
• the side elevation: looking from the side.

Example: describe the plan and front elevation of a square-based pyramid.

1. Plan: from above, a square with lines from each corner to the centre, where the top point is
2. Plan: a square with its diagonals drawn
3. Front elevation: from the front, the sloping faces meet at the top
4. Front elevation: a triangle

Example: a cylinder stands upright on a table. Describe its plan and front elevation.

1. Plan: a circle
2. Front elevation: a rectangle